In systems operating under uncertainty, the uncertain parameters are also random variables, having distributions with most of their characteristics unidentified (except for some information about them that is known a priori, for example, independence of parameters, bounds of permissible values, and symmetry). This paper presents a probabilistic approach to an important problem in system analysis encountered in systems operating under uncertainty. The problem concerns the choice of a system performance criterion.

The problem is how to measure the system performance considering all of the available prior information on the system parameters. The paper deals with this problem by comparing a classical approach based on the worst value of the loss function, called the loss maximum, and a more sophisticated approach based on the quantile performance criteria theory, called the worst quantile. The latter is proven to be much more optimistic on average, since it ignores some unlikely pessimistic combinations of the parameters, especially when their number is large.

After a rather brief and informal introduction, the paper proceeds with the formal statement of the problem by defining the two criteria (loss maximum and worst quantile), and also two functions for comparing them. The rest of the paper presents, in four subsequent sections, the theoretical results concerning the estimation of the two comparison functions. The proofs are given in the appendix.

In general, the paper is highly theoretical, and requires a very strong mathematical background in probability measure theory for a thorough study. The conclusions section is very brief, and there is no discussion of possible practical applications to real systems. This is clearly a very interesting paper, recommended to researchers working on the theoretical aspects of system performance.